one variable, linear regression

## [1] "*************************************************************"
## [1] "one variable, linear regression"
## [1] "bSigmaBest 6"
## [1] "naive effects model"
## [1] "one variable, linear regression naive effects model fit model:"
## 
## Call:
## lm(formula = formulaL, data = trainData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3721 -0.6891 -0.0037  0.6848  3.7826 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.20623    0.02260   9.125   <2e-16 ***
## x1           1.00000    0.03685  27.137   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 1998 degrees of freedom
## Multiple R-squared:  0.2693, Adjusted R-squared:  0.269 
## F-statistic: 736.4 on 1 and 1998 DF,  p-value: < 2.2e-16
## 
## [1] "one variable, linear regression naive effects model train rmse 1.01025938596012"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                grob
## 1 1 (2-2,1-1) arrange      gtable[layout]
## 2 2 (2-2,2-2) arrange      gtable[layout]
## 3 3 (3-3,1-1) arrange      gtable[layout]
## 4 4 (3-3,2-2) arrange      gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.140]
## [1] "one variable, linear regression naive effects model test rmse 0.999915402747535"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                grob
## 1 1 (2-2,1-1) arrange      gtable[layout]
## 2 2 (2-2,2-2) arrange      gtable[layout]
## 3 3 (3-3,1-1) arrange      gtable[layout]
## 4 4 (3-3,2-2) arrange      gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.293]
## [1] "effects model, sigma= 6"
## [1] "one variable, linear regression effects model, sigma= 6 fit model:"
## 
## Call:
## lm(formula = formulaL, data = trainData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3911 -0.6877 -0.0039  0.6858  3.7951 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.20587    0.02262   9.102   <2e-16 ***
## x1           1.00844    0.03726  27.064   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 1998 degrees of freedom
## Multiple R-squared:  0.2683, Adjusted R-squared:  0.2679 
## F-statistic: 732.5 on 1 and 1998 DF,  p-value: < 2.2e-16
## 
## [1] "one variable, linear regression Laplace noised 6 train rmse 1.0109902603753"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                grob
## 1 1 (2-2,1-1) arrange      gtable[layout]
## 2 2 (2-2,2-2) arrange      gtable[layout]
## 3 3 (3-3,1-1) arrange      gtable[layout]
## 4 4 (3-3,2-2) arrange      gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.446]
## [1] "one variable, linear regression Laplace noised 6 test rmse 1.00200195619019"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                grob
## 1 1 (2-2,1-1) arrange      gtable[layout]
## 2 2 (2-2,2-2) arrange      gtable[layout]
## 3 3 (3-3,1-1) arrange      gtable[layout]
## 4 4 (3-3,2-2) arrange      gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.599]
## [1] "effects model, jacknifed"
## [1] "one variable, linear regression effects model, jackknifed fit model:"
## 
## Call:
## lm(formula = formulaL, data = trainData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3933 -0.6946 -0.0039  0.6875  3.7985 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   0.2062     0.0227   9.084   <2e-16 ***
## x1            0.9871     0.0370  26.682   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.015 on 1998 degrees of freedom
## Multiple R-squared:  0.2627, Adjusted R-squared:  0.2623 
## F-statistic:   712 on 1 and 1998 DF,  p-value: < 2.2e-16
## 
## [1] "one variable, linear regression jackknifed train rmse 1.01481235978284"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                grob
## 1 1 (2-2,1-1) arrange      gtable[layout]
## 2 2 (2-2,2-2) arrange      gtable[layout]
## 3 3 (3-3,1-1) arrange      gtable[layout]
## 4 4 (3-3,2-2) arrange      gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.752]
## [1] "one variable, linear regression jackknifed test rmse 1.00008428967326"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                grob
## 1 1 (2-2,1-1) arrange      gtable[layout]
## 2 2 (2-2,2-2) arrange      gtable[layout]
## 3 3 (3-3,1-1) arrange      gtable[layout]
## 4 4 (3-3,2-2) arrange      gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.905]

## [1] "********"
## [1] "one variable, linear regression JackknifeModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9870  0.9981  1.0030  1.0030  1.0080  1.0160 
## [1] 0.007085046
## [1] "********"
## [1] "********"
## [1] "one variable, linear regression NaiveModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9872  0.9982  1.0030  1.0030  1.0080  1.0160 
## [1] 0.007089328
## [1] "********"
## [1] "********"
## [1] "one variable, linear regression NoisedModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9872  0.9986  1.0030  1.0030  1.0090  1.0270 
## [1] 0.007298878
## [1] "********"

## [1] "*************************************************************"

one variable plus noise variable, linear regression

## [1] "*************************************************************"
## [1] "one variable plus noise variable, linear regression"
## [1] "bSigmaBest 20"
## [1] "naive effects model"
## [1] "one variable plus noise variable, linear regression naive effects model fit model:"
## 
## Call:
## lm(formula = formulaL, data = trainData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9216 -0.6181  0.0055  0.6225  3.5298 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.20622    0.02058   10.02   <2e-16 ***
## x1           0.83459    0.03452   24.17   <2e-16 ***
## n1           0.78131    0.03844   20.33   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9203 on 1997 degrees of freedom
## Multiple R-squared:  0.3946, Adjusted R-squared:  0.394 
## F-statistic: 650.8 on 2 and 1997 DF,  p-value: < 2.2e-16
## 
## [1] "one variable plus noise variable, linear regression naive effects model train rmse 0.919591353886876"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.1348]
## [1] "one variable plus noise variable, linear regression naive effects model test rmse 1.12246743812363"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.1501]
## [1] "effects model, sigma= 20"
## [1] "one variable plus noise variable, linear regression effects model, sigma= 20 fit model:"
## 
## Call:
## lm(formula = formulaL, data = trainData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4443 -0.6800  0.0048  0.6893  3.6971 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.220924   0.022714   9.726   <2e-16 ***
## x1          0.996705   0.037206  26.789   <2e-16 ***
## n1          0.002196   0.001237   1.775   0.0761 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.014 on 1997 degrees of freedom
## Multiple R-squared:  0.2654, Adjusted R-squared:  0.2647 
## F-statistic: 360.8 on 2 and 1997 DF,  p-value: < 2.2e-16
## 
## [1] "one variable plus noise variable, linear regression Laplace noised 20 train rmse 1.01294930678851"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.1654]
## [1] "one variable plus noise variable, linear regression Laplace noised 20 test rmse 1.01405603472151"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.1807]
## [1] "effects model, jacknifed"
## [1] "one variable plus noise variable, linear regression effects model, jackknifed fit model:"
## 
## Call:
## lm(formula = formulaL, data = trainData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3986 -0.6920 -0.0077  0.6877  3.8126 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.20643    0.02268   9.101   <2e-16 ***
## x1           0.98425    0.03698  26.614   <2e-16 ***
## n1          -0.07739    0.03479  -2.224   0.0262 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.014 on 1997 degrees of freedom
## Multiple R-squared:  0.2645, Adjusted R-squared:  0.2638 
## F-statistic: 359.2 on 2 and 1997 DF,  p-value: < 2.2e-16
## 
## [1] "one variable plus noise variable, linear regression jackknifed train rmse 1.01355772650768"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.1960]
## [1] "one variable plus noise variable, linear regression jackknifed test rmse 1.00913108707443"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.2113]

## [1] "********"
## [1] "one variable plus noise variable, linear regression JackknifeModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9817  0.9976  1.0030  1.0030  1.0070  1.0280 
## [1] 0.007405488
## [1] "********"
## [1] "********"
## [1] "one variable plus noise variable, linear regression NaiveModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.101   1.122   1.132   1.133   1.143   1.184 
## [1] 0.0138748
## [1] "********"
## [1] "********"
## [1] "one variable plus noise variable, linear regression NoisedModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9865  1.0020  1.0070  1.0080  1.0130  1.0360 
## [1] 0.008722391
## [1] "********"

## [1] "*************************************************************"

one variable plus noise variable, diagonal regression

## [1] "*************************************************************"
## [1] "one variable plus noise variable, diagonal regression"
## [1] "bSigmaBest 33"
## [1] "naive effects model"
## [1] "one variable plus noise variable, diagonal regression naive effects model fit model:"
##       x1       n1 
## 1.000005 1.000333 
## [1] "one variable plus noise variable, diagonal regression naive effects model train rmse 0.958540237968956"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.2556]
## [1] "one variable plus noise variable, diagonal regression naive effects model test rmse 1.20618715828122"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.2709]
## [1] "effects model, sigma= 33"
## [1] "one variable plus noise variable, diagonal regression effects model, sigma= 33 fit model:"
##          x1          n1 
## 0.956214908 0.001476339 
## [1] "one variable plus noise variable, diagonal regression Laplace noised 33 train rmse 1.04489536941947"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.2862]
## [1] "one variable plus noise variable, diagonal regression Laplace noised 33 test rmse 1.04773767097596"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.3015]
## [1] "effects model, jacknifed"
## [1] "one variable plus noise variable, diagonal regression effects model, jackknifed fit model:"
##         x1         n1 
##  0.9871528 -0.1088369 
## [1] "one variable plus noise variable, diagonal regression jackknifed train rmse 1.03458802692346"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.3168]
## [1] "one variable plus noise variable, diagonal regression jackknifed test rmse 1.03176880530955"

## TableGrob (3 x 2) "arrange": 5 grobs
##   z     cells    name                 grob
## 1 1 (2-2,1-1) arrange       gtable[layout]
## 2 2 (2-2,2-2) arrange       gtable[layout]
## 3 3 (3-3,1-1) arrange       gtable[layout]
## 4 4 (3-3,2-2) arrange       gtable[layout]
## 5 5 (1-1,1-2) arrange text[GRID.text.3321]

## [1] "********"
## [1] "one variable plus noise variable, diagonal regression JackknifeModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9976  1.0170  1.0220  1.0220  1.0260  1.0430 
## [1] 0.007842663
## [1] "********"
## [1] "********"
## [1] "one variable plus noise variable, diagonal regression NaiveModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.178   1.207   1.218   1.218   1.231   1.277 
## [1] 0.01783066
## [1] "********"
## [1] "********"
## [1] "one variable plus noise variable, diagonal regression NoisedModel"
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9983  1.0220  1.0280  1.0290  1.0350  1.0890 
## [1] 0.01197814
## [1] "********"

## [1] "*************************************************************"